Ratios

Ratios are used to compare multiple amounts of quantities to each other. Common examples are:

• Flour to water
• Gears in a bicycle
• Class composition – how many students study maths compared to English

Things to remember with ratios:

• Part A : Part B or Part A to Part B
• Part A + Part B = Total. For example: 5:15; Total number 20 and 2:4:6; Total number 12.
• You can simplify if sharing common factors: 2:4:6 => 1:2:3

Speed

Formula to calculate is speed is distance divided by time.

Remember there are 3 components (speed, distance and time) and easiest way to think about it is the speedometer.

For example, the speedometer says you're travelling at 5km/hour and then at 50km/hour. Which is faster? The latter because you travel more in the same time frame and to do that, you have to go faster!

Let’s work out the following questions together (see video):

Jess drives at an average speed of 60 km/h from Sydney to Orange which is approximately 360km. How long does she take?

Anders cycles at an average speed of 5m/h. If he cycles for 3 hours, how far has he gone?

Speed and ratio questions are heavily dependent on practice questions so watch the video carefully as we go through more example questions.

Example Question/s

Watch video for explanation of the following question/s:

What is the speed in m/s of a bicycle that travels 9 km in 25 minutes?

A 3 m/s B 6 m/s C 9 m/s D 12 m/s E None of these

The next 2 questions refer to the following information:

Jake has two rotating wheels.

When the larger wheel turns 15 times the smaller wheel turns 60 times. Assuming that their rotating speed are the same, what is the circumference of the larger wheel if the smaller wheel has a circumference of 62 cm?

A 186 cm B 248 cm C 630 cm D 992 cm

If you let the larger wheel roll on the ground, how far will it travel if it turns 50 times?

A 48 metres B 72 metres C 96 metres D 124 metres

Key Rules to remember:

• Add ratio parts together to get the ‘whole’ and you can simplify ratios to make it easier to work with them.
• Speed = distance / time

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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